Addition
Students master addition by connecting concrete counting to abstract number relationships. The progression from 3 + 2 = 5 with manipulatives to multi-digit problems like 247 + 186 = 433 requires systematic instruction aligned with CCSS.1.OA and CCSS.2.NBT standards.
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Why it matters
Addition forms the foundation for all mathematical operations students encounter throughout their academic journey. In real-world contexts, children use addition to calculate lunch money (3 dollars + 2 dollars = 5 dollars), determine total items when shopping (12 apples + 8 oranges = 20 pieces of fruit), and solve time problems (30 minutes + 15 minutes = 45 minutes). Research shows students who master single-digit addition facts by grade 2 demonstrate 40% better performance in later mathematics courses. The skill transfers directly to measurement, where students add 2 feet + 3 feet = 5 feet, and to data analysis when combining survey results like 25 responses + 18 responses = 43 total responses. Strong addition skills enable students to tackle word problems confidently and build number sense essential for algebra readiness.
How to solve addition
Addition — how to
- Line up digits by place value (ones under ones, tens under tens).
- Add each column starting from the right.
- If a column sum is 10+, carry the tens digit to the next column.
Example: 27 + 38: 7+8=15, write 5 carry 1. 2+3+1=6. Answer: 65.
Worked examples
There are 3 books on the table and 3 books on the floor. How many altogether?
Answer: 6
- Look at the two numbers → 3 + 3 — We have 3 and 3. Adding means putting things together. Imagine you have 3 candies and someone gives you 3 more.
- Count on from the bigger number → 3 ... +3 ... = 6 — Start at 3 and count up 3 more: 4, 5, 6. We land on 6!
- Write the answer → 3 + 3 = 6 — When we put 3 and 3 together we get 6. That is our answer!
Solve: 9 + 17 -----
Answer: 26
- Look at the two numbers → 9 + 17 — We have 9 and 17. Adding means putting things together. Imagine you have 9 candies and someone gives you 17 more.
- Count on from the bigger number → 17 ... +9 ... = 26 — Start at 17 and count up 9 more: 18, 19, 20, 21, 22, 23, 24, 25, 26. We land on 26!
- Write the answer → 9 + 17 = 26 — When we put 9 and 17 together we get 26. That is our answer!
70 + 17 = _______
Answer: 87
- Look at what we are adding → 70 + 17 — We need to add 70 and 17. Think of it like combining two groups of things into one big group.
- Add the ones (right) column → 0 + 7 = 7 — Start with the ones place (the last digit). 0 + 7 = 7. That fits in one digit, so we write it down.
- Add the tens (left) column → 7 + 1 = 8 — Now the tens place: 7 + 1 = 8. This gives us 80 in the tens spot.
- Put the digits together → 70 + 17 = 87 — Tens (80) and ones (7) together make 87.
- Check: does our answer make sense? → 70 + 17 = 87 ✓ — A quick check: 70 is close to 70 and 17 is close to 20, so roughly 70 + 20 = 90. Our answer 87 is in that neighbourhood, so it looks right!
Common mistakes
- ✗Students reverse the order when adding vertically, writing 25 + 17 = 32 instead of 42 because they add 2 + 1 = 3 in the tens place first.
- ✗Children forget to carry when column sums exceed 9, calculating 38 + 27 = 515 instead of 65 by writing both digits in the answer.
- ✗Students misalign place values, adding 134 + 27 as if it were 134 + 270, getting 404 instead of the correct 161.
- ✗Young learners double-count the starting number when counting on, finding 6 + 3 = 10 instead of 9 by counting '6, 7, 8, 9, 10' including the initial 6.
Practice on your own
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